New operations for informative combination of two partial order relations with illustrations on pollution data

We discuss various ways in which to construct and process partial order relations or partially ordered sets (posets) in the context of ranking objects on the basis of multiple criteria. Oftentimes, it is undesirable or even impossible to devise a weighting scheme to compute a final score on the basis of the criteria. An alternative is then to restrict oneself to the information contained in the partial ordering of all objects implied by the criteria. We will consider some ways in which one can exploit partial order relations to determine a ranking of a collection of objects. More exactly, we will examine how to combine information coming from two sources, both for the case in which the sources are considered to be equally important, as well as for the case in which one source of information should take priority. We illustrate the concepts on pollution data coming from 59 regions in Baden-Württemberg.